Problem 1. If f (x) has an inverse function f-1(x), could either the graph of f (x) or the graph of f (x) be symmetric with respect to the y-axis? Explain your reasoning or use an example to illustrate your answer. Problem 2. Let f (x) = In ( + 9) and g(x) = . Find the domain of (fog) (x). Write your answer in interval notation. Problem 3. For the function f (x) = 6x2 - x - 2, evaluate and fully simplify each of the following: a) f ( x + h ) = b ) f(xth ) - f (x) = h Instructions: Simplify answers as much as possible. Expressions such as 3(x+5) and (x + h)2 should be expanded. Also, combine like terms, so 7x+3x should be written as 10x. Problem 4. a) Find the vertex, axis of symmetry, and intercepts, if any, of the function f (x) = -x2 - 6x - 10. b) Use this information to graph the function. Label key points on the graph. c) State the domain and range of f(x). d) Find the intervals where the function is increasing/decreasing. e) Does f(x) have local maxima/minima? If so, find those local maxima/minima and indicate the values of x where they attained. Problem 5. Find the standard form of the equation of the circle x2 + y2 - 2x + 12y + 12 = 0. Then, state the center and radius of the circle. Problem 6. Sketch a graph of -2x - 7, if x 1. What is the domain of f (x)? What is the range of f (x)? Problem 7. a) Describe the transformation(s) that can be applied to the function g(x) = ex to obtain the graph of f (x) = e-*+ 7. b) State the domain and range of f(x). c) Sketch the graph of f(x)